Geometrical surface-models of anatomical structures are commonly represented by three-dimensional (3D) triangular surface meshes. Such a 3D triangular surface mesh representation of an object generally works well in case that the dataset from which the surfaces mesh is reconstructed represents a 2-manifold, i.e. can be divided into voxels lying “inside” or “outside” of the object.
However, many clinical applications require the representation and segmentation of several structures, like adjacent organs arranged next to each other, thus representing a non-2-manifold. Prominent examples are the heart with its heart chambers and heart valves, or the pelvic region housing bladder, prostate and rectum. In such a case a triangle of the 3D surface mesh may have more than three neighbouring triangles, in particular in areas where surfaces of the objects form so called 3D T-junction, i.e. a junction where two or more different objects meet each other. In particular, in such a 3D T-junction case the image features are ambiguous and lead to segmentation errors when the 3D triangular surface mesh is constructed. Thus, the generation of such surface models cannot be done with standard triangulation methods.
Image segmentation using so called deformable models are an important technology in medical applications. This technique can provide shape information of the single objects adjacent to each other, thus reducing ambiguity in the image content and leading to more robust segmentation results. Typical shapes of organs are often represented by triangular surface meshes. The robustness of these methods can be improved by adding information about special relationships of multiple objects. For example, the adding can be done by representing multiple objects with common or touching boundaries with a single mesh structure.
Combining separately constructed triangular meshes using Boolean geometrical operations is cumbersome and requires usually manual interactions. Another way to handle the construction of smooth non-2-manifold meshes is described in “Constructing Smooth Non-Manifold Meshes of Multi-Labeled Volumetric Datasets” from Bernhard Reitinger et al., Conference Proceedings WSCG 2005, Jan. 31-Feb. 4, 2005. Reitinger et al. relates to the construction of smooth meshes out of multilabelled datasets by subdividing cells comprising two or more materials, which corresponds to the case of the touching of two or more organs in the human body. In the two-dimensional (2D) case the subdivision is achieved by inserting a cell mid-point. Additionally, segment mid-points are generated if the labels of two adjacent so-called voxels (volume pixels) are different. For each generated segment mid-point a new segment (line) to the cell mid-point is generated. The same strategy of inserting additional cell mid-points can be used for the 3D case.
However, there may be the need for another method for a triangulation method of multiple objects.